This was written in response to: https://twitter.com/hillelogram/status/1227118562373963776
People mix the predicate "If a directed graph is a tree, it's a DAG" with the proposition "For all directed graphs, if a directed graph is a tree, it's a DAG".
First, for simplification: let's assume we're talking here about all graphs in the world with up to 10 nodes to be able to enumerate them. Also, note that we're talking about directed, not undirected, graphs.
To prove the proposition "For all..." is true, which is "(For graph G1, if it's a tree, it's a DAG) AND (For graph G2, if it's a tree, it's a DAG) AND...", since it's ANDs, we need to prove (For graph G1, if...) is true and we need to prove (For graph G2, if...) is true, ... etc.